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# Technical Progress Function (TPF)

## What Is the Technical Progress Function?

The technical progress function (TPF) is a part of a macroeconomic growth model that accounts for the impact of technology and technological progress on the total amount of economic output a society can and does produce as well as the productivity of the factors of production that a society employs. Previous models of macroeconomic growth focused on factors such as natural resource endowments, a growing labor force, or the accumulation of capital goods and equipment to explain economic growth and development. In the 20th century the role of technical improvements in how these various production factors could be combined more efficiently to improve their productivity became widely recognized among economists as a key to economic growth. The incorporation of a TPF into models of macroeconomic growth by several different economists brought this recognition into formal economic modeling.

The TPF in a given macroeconomic model specifies in mathematical terms the relationship between technological progress and increase in output. The specific forms and structure of the TPF may vary from one macroeconomic model to another, but they generally show that an increase in the rate of technical progress is the most—or one of the most—important factor(s) in promoting overall productivity and economic growth. Technological progress can be an important factor in a country’s economic growth because it helps a nation produce more through the use of better technology on the input side of the production equation.

Based on these macroeconomic models, econometric techniques can be used to estimate the influence of technological progress on total economic output empirically through the use of a regression model. Thus, rather than looking at economic production growth purely in terms of input allocation efficiency, the technical progress function provides a way to measure technological progress as a contributor to final production overall.

### Key Takeaways

• The TPF is a component of a macroeconomic model studying how different factors influence total production.
• The TPF measures how much economic growth can be attributed to technological progress innovation in a country.
• Technical progress can show up as either embodied in new equipment or disembodied in productivity gains from new innovations unrelated to equipment.

## Understanding the TPF

The TPF is a component of a multifactor regression model used to understand total production and how different variables affect total production. In a basic production regression, the output is explained by the level of efficiency in which basic variables are allocated to production. For example, labor and machinery are two basic variables that influence production.

With more in depth analysis, economic statisticians may seek to break out technological progress into two elements. The two main elements are usually:

• Embodied technical progress: Improved technology which is attributed to investments in new equipment. New technical changes that are made are embodied in the equipment.
• Disembodied technical progress: Improved technology which results in output increases without investing in new equipment.

The technical progress function is an added variable to a production regression analysis. Basically, it is an additional function of the equation that provides insight on technological contributions to production that are not explained by any of the other basic inputs. Generally, as technological progress increases, more production is attributed to technical progress within the production equation and less to the other variables.

## The Solow Residual

Robert Solow received a Nobel Prize for his work on concepts of technical progress function, also known as the Solow Residual and total factor productivity (TFP). Solow laid out the growth model used to understand productivity with his model detailing the different functions that influence productivity. Solow’s model includes the functions of capital, labor, and technological progress. Later researchers have modified Solow's model for the inclusion of additional variables, such as human capital.

In Solow’s model, the TPF is the reading on how much technological progress is influencing the total output.

When using the model for the years 1909-49 in the United States, Solow found that only one-eighth of the increase in labor productivity in the United States could be attributed to increased capital. The rest was a result of technical progress in how labor and capital were used. America, in other words, became great because of American know-how and innovation.

Total factor productivity can be affected by a variety of influences. While all under the umbrella of technological progress, influences can include tech, cultural factors, and new economic efficiencies. As such, the technical progress function and TFP can also be used to analyze differences in countries’ technological influences and technological progress.

### Article Sources

Investopedia requires writers to use primary sources to support their work. These include white papers, government data, original reporting, and interviews with industry experts. We also reference original research from other reputable publishers where appropriate. You can learn more about the standards we follow in producing accurate, unbiased content in our editorial policy.
1. The Nobel Prize. "The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1987." Accessed Aug. 25, 2021.

2. The Review of Economics and Statistics. "Technical Change and the Aggregate Production Function." Accessed Aug. 25, 2021.

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